Gaussian Pyramid

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# Gaussian Pyramid - PowerPoint PPT Presentation

Gaussian Pyramid. Slides from Alexei Efros. Sampling. Good sampling: Sample often or, Sample wisely. Bad sampling: see aliasing in action!. Gaussian pre-filtering. G 1/8. G 1/4. Gaussian 1/2. Solution: filter the image, then subsample

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### Gaussian Pyramid

Slides from Alexei Efros

Sampling
• Good sampling:
• Sample often or,
• Sample wisely
• see aliasing in action!
Gaussian pre-filtering

G 1/8

G 1/4

Gaussian 1/2

• Solution: filter the image, then subsample
• Filter size should double for each ½ size reduction. Why?
Subsampling with Gaussian pre-filtering

Gaussian 1/2

G 1/4

G 1/8

• Solution: filter the image, then subsample
• Filter size should double for each ½ size reduction. Why?
• How can we speed this up?
Compare with...

1/2

1/4 (2x zoom)

1/8 (4x zoom)

Why does this look so crufty?

Image Pyramids
• Known as a Gaussian Pyramid [Burt and Adelson, 1983]
• In computer graphics, a mip map [Williams, 1983]
• A precursor to wavelet transform

A bar in the big images is a hair on the zebra’s nose; in smaller images, a stripe; in the smallest, the animal’s nose

Figure from David Forsyth

Gaussian pyramid construction

• Repeat
• Filter
• Subsample
• Until minimum resolution reached
• can specify desired number of levels (e.g., 3-level pyramid)
• The whole pyramid is only 4/3 the size of the original image!
Gaussian pyramid construction

is similar to Gaussian

Laplacian Pyramid

Gaussian Pyramid

• Laplacian Pyramid decomposition
• Created from Gaussian pyramid by subtraction
Laplacian Pyramid

Gaussian Pyramid

• Laplacian Pyramid decomposition
• Created from Gaussian pyramid by subtraction
What are they good for?
• Improve Search
• Search over translations
• Like homework
• Classic coarse-to-fine stategy
• Search over scale
• Template matching
• E.g. find a face at different scales
• Precomputation
• Need to access image at different blur levels
• Useful for texture mapping at different resolutions (called mip-mapping)
• Image Processing
• Editing frequency bands separetly
• E.g. image blending… next time!